Rob Bayer
Math 55 Worksheet
June 29, 2009
Instructions
•
Introduce yourselves! Despite popular belief, math is in fact a team sport!
•
Find some blackboard space, a piece of chalk, and decide who will be your ﬁrst scribe.
•
Do the problems below, having a diﬀerent person be the scribe for each one.
•
Try to work out the problems as a group, but feel free to ﬂag me down if you run into a wall.
Functions and Sets
1. Determine whether each of the following are injections, surjections, bijections, or none of the three.
(a)
f
:
R
→
R
,f
(
x
) = 3
x

2
(b)
f
:
R
→
Z
,f
(
x
) =
b
x
c
(c)
f
:
N
→
N
,f
(
n
) =
n
+ 1
(d)
f
:
R
→
R
,f
(
x
) =
x
(
x

3)(
x
+ 2)
2. Decide whether each of the following are true or false. For those that are true, prove it. For those that are
false, provide a counterexample.
(a) If
f,g
are injective, then
f
◦
g
is
(b) If
f,g
are surjective, then
f
◦
g
is
(c) If
f
◦
g
is injective, then
f
is.
(d) If
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 Summer '08
 STRAIN
 Math, Inverse function, Surjective function, popular belief, Rob Bayer, blackboard space

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